How do you differentiate f(x) =(2+x )( 2-3x) using the product rule?

2 Answers
Jun 7, 2017

-6x -4

Explanation:

f(x) = (2 + x)(2 - 3x)

let say u = (2 + x), then u' = 1 and v =(2 - 3x), then v' = -3

f'(x) = uv' + vu'

f'(x) = (2 + x)(-3) +(2 - 3x)(1)

f'(x) = -6 -3x +2 - 3x = -6x -4

Jun 7, 2017

-6x-4

Explanation:

If we want to differentiate f(x)=(2+x)(2-3x) using the product rule we use the following (f')(g)+(g')(f). Where f is your first term (2+x) and g is your second term (2-3x). So, we take the d/dx of f which is 1 using the power rule nx^(n-1) keep in mind that the d/dx of a constant is zero, while g remains the same. At this point what we have is 1(2-3x) now we take the d/dx of g which is -3, f remains the same.

After we have derived the equation we now have the following:

1(2-3x)-3(2+x)

Go ahead distribute and simplify:

2-3x-6-3x=-6x-4

Our final answer is -6x-4.